Art Rapp published his fanzine in Saginaw, Michigan from April 1947 til September 1950. Rapp was a member of the Michigan Science Fantasy Society. After a meeting of the group in November of 1949, two members set off a bomb in the front yard of Rapp's home. Police were called and neighbours gathered, and according to Rapp in an open letter he wrote of the incident, the bomb was heard from two miles away. Immediately after, Rapp quit MSFS but didn't end his zine till the next year, when he left the U.S. for military duty in Korea. He then turned the zine over to F. Towner Laney and Charles Burbee to edit. They put out two issues.

In 1983, Rapp resumed publishing Spacewarp.

Certain columns in Spacewarp, such as Redd Bogg's "File 13" became famous in SF fandom over time. As well, it included art and cartoons by Ray Nelson, writer of the short story, 8 o'clock in the Morning, which was later made into the film They Live by John Carpenter.